arXiv subjects

Felix C. Binder

Publications and source records attributed to Felix C. Binder.

At least 19 recordsLinked to original sources

arXiv2026

Energetic Costs of Subspace Quantum Error Correction

Quantum error correction acts as an entropy pump, transferring noise-induced uncertainty from a protected quantum system into syndrome information stored in an auxiliary memory. Repeated operation requires this memory to be cleared which unavoidably contributes to the energetic cost of error correction. Here, we characterise this contribution for subspace quantum error-correcting codes and identify how it depends on the joint structure of the code, the noise, and the representation of the retained syndrome information. Starting from the Knill-Laflamme conditions, we construct an effective syndrome state whose von Neumann entropy sets a lower bound on the ideal work required to maintain a reusable syndrome register. Projective syndrome readout generally generates additional entropy, and we quantify the resulting gap through measurement inefficiency. We then specialise to stabiliser codes under independent local Pauli noise and analyse two classical levels of syndrome representation. At the level of abstract error labels, degeneracies among single-qubit errors reduce the leading-order entropy of processed recovery labels. At the parity-check level, lower-weight checks reduce the marginal entropy generated by individual measurement outcomes in the low-noise regime. We identify the additional burden associated with retaining and separately erasing these outcomes as a bit-level inefficiency, and illustrate both costs for the five-qubit, Steane, generalised Shor, and rotated surface codes. Our results establish a hierarchy of syndrome-memory energetic costs and identify the code, noise, and measurement structures that control the ideal thermodynamic burden of subspace quantum error correction.

quant-ph↗

arXiv2026

The Trinity of Markovian Quantum Thermodynamics: Unifying the Axiomatic, Microscopic, and Operational Paradigms

Thermodynamics imposes fundamental constraints on the evolution of quantum systems. These constraints and their dynamical consequences have been formulated within distinct paradigms, including axiomatic approaches based on quantum master equations, microscopic descriptions of open-system dynamics, and operational formulations rooted in resource theories. While each perspective has yielded important insights into thermodynamically consistent quantum dynamics, their precise relationship has remained unresolved. Here we establish the exact equivalence of these three paradigms in the Markovian regime. We prove that thermal Lindbladians satisfying Markovianity, time-translation symmetry, and quantum detailed balance are precisely those admitting a microscopic realisation as an energy-conserving thermal collision model and, equivalently, those generating Markovian thermal operations. This unifies the existing approaches to Markovian quantum thermodynamics and identifies its dynamical underpinnings. We further provide an explicit microscopic protocol for simulating thermal Markovian processes with controlled finite-time simulation errors. We illustrate its applicability by providing faithful thermal collision-model implementations of a qubit thermalising in a bosonic environment and of a three-level autonomous thermal machine. In the latter case, the protocol gives rise to a finite-stroke thermal engine that not only reproduces the continuous-time dynamics but also its steady-state thermodynamic performance. As a whole, these results establish a unified foundation for Markovian quantum thermodynamics, showing that its axiomatic, microscopic, and operational formulations are exactly equivalent and providing a universal protocol for implementing thermal processes and machines.

quant-ph↗

arXiv2026

Distinguishing quantum processes with bounded coherent memory

Distinguishing multi-time quantum processes is a fundamental task underlying the diagnosis, benchmarking, and learning of temporally correlated quantum dynamics. The standard benchmark for distinguishing two processes is the strategy-norm distance, which optimizes over arbitrary adaptive probing strategies but can require large coherent memory and time-dependent control. We introduce machines for autonomous distinction~($\mathsf{MAD}$s): probing strategies that apply the same quantum instrument at each time step, retain the full classical outcome record, and carry a coherent memory of dimension $d_A$. Optimizing over these strategies defines a memory-parametrized distinguishability measure, $d^{(N)}_{\mathsf{MAD}}(\mathbf{P}^N,\mathbf{Q}^N;d_A)$. We show that the resulting hierarchy is monotone in coherent memory and complete at finite times. Specifically, any admissible $N$-step probing strategy can be compiled into a single $\mathsf{MAD}$ with an internal counter and sufficiently large coherent memory, so the hierarchy saturates the strategy-norm benchmark. For recurrent processes generated by repeated system--environment interactions, we derive a single-step description that separates the generation of new distinguishing information from the propagation and decay of information generated at earlier times. Numerical results in a repeated-interaction model show that increasing coherent memory systematically improves the $\mathsf{MAD}$ success probability and closes the gap to the strategy-norm distance while remaining substantially more tractable to evaluate. $\mathsf{MAD}$ distinguishability therefore provides an operational and scalable framework for quantifying what can be learned about genuinely multi-time quantum processes with bounded coherent memory.

quant-ph↗

arXiv2026

Accelerating qubit reset through the Mpemba effect

Passive qubit reset is a key primitive for quantum information processing, whereby qubits are initialized by allowing them to relax to their ground state through natural dissipation, without the need for active control or feedback. However, passive reset occurs on timescales that are much longer than those of gate operations and measurements, making it a significant bottleneck for algorithmic execution. Here, we show that this limitation can be overcome by exploiting the Mpemba effect, originally indicating the faster cooling of hot systems compared to cooler ones. Focusing on the regime where coherence times exceed energy relaxation times ($T_2 > T_1$), we propose a simple protocol based on a single entangling two-qubit gate that converts local single-qubit coherences into fast-decaying global two-qubit coherences. This removes their overlap with the slowest decaying Liouvillian mode and enables a substantially faster relaxation to the ground state. For realistic parameters, we find that our protocol can reduce reset times by up to $50\%$ compared to standard passive reset. We analyze the robustness of the protocol under non-Markovian noise, imperfect coherent control and finite temperature, finding that the accelerated reset persists across a broad range of realistic error sources. Finally, we present an experimental implementation of our protocol on an IQM superconducting quantum processor. Our results demonstrate how Mpemba-like accelerated relaxation can be harnessed as a practical tool for fast and accurate qubit initialization.

quant-ph↗

arXiv2026

Average Equilibration Time for Gaussian Unitary Ensemble Hamiltonians

Understanding equilibration times in closed quantum systems is essential for characterising their approach to equilibrium. Chaotic many-body systems are paradigmatic in this context: they are expected to thermalise according to the eigenstate thermalisation hypothesis and exhibit spectral properties well described by random matrix theory (RMT). While RMT successfully captures spectral correlations, its ability to provide quantitative predictions for equilibration timescales has remained largely unexplored. Here, we study equilibration within RMT using the framework of equilibration as dephasing, focusing on closed systems whose Hamiltonians are drawn from the Gaussian unitary ensemble (GUE). We derive an analytical expression that approximates the average equilibration time of the GUE and show that it is independent of both the initial state and the choice of observable, a consequence of the rotational invariance of the GUE. Numerical simulations confirm our analytical expression and demonstrate that our approximation is in close agreement with the true average equilibration time of the GUE. We find that the equilibration time decreases with system size and vanishes in the thermodynamic limit. This unphysical result indicates that the true equilibration timescale of realistic chaotic many-body systems must be dominated by physical features not captured by random matrix ensembles -- the GUE in particular.

quant-ph↗

arXiv2026

Digitally Optimized Initializations for Fast Thermodynamic Computing

Thermodynamic computing harnesses the relaxation dynamics of physical systems to perform matrix operations. A key limitation of such approaches is the often long thermalization time required for the system to approach equilibrium with sufficient accuracy. Here, we introduce a hybrid digital-thermodynamic algorithm that substantially accelerates relaxation through optimized initializations inspired by the Mpemba effect. In the proposed scheme, a classical digital processor efficiently computes an initialization that suppresses slow relaxation modes, after which the physical system performs the remaining computation through its intrinsic relaxation dynamics. We focus on overdamped Langevin dynamics for quadratic energy landscapes, analyzing the spectral structure of the associated Fokker-Planck operator and identifying the corresponding optimal initial covariances. This yields a predictable reduction in thermalization time, determined by the spectrum of the encoded matrix. We derive analytic expressions for the resulting speedups and numerically analyze thermodynamic implementations of matrix inversion and determinant computation as concrete examples. Our results show that optimized initialization protocols provide a simple and broadly applicable route to accelerating thermodynamic computations.

cond-mat.stat-mech↗

arXiv2026

Thermodynamic Constraints on the Emergence of Intersubjectivity in Quantum Systems

Ideal quantum measurement requires divergent thermodynamic resources. This is a consequence of the third law of thermodynamics, which prohibits the preparation of the measurement pointer in a fully erased, pure state required for the acquisition of perfect, noiseless measurement information. In this work, we investigate the consequences of finite resources in the emergence of intersubjectivity as a model for measurement processes with multiple observers. Here, intersubjectivity refers to a condition in which observers agree on the observed outcome (agreement), and their local random variables exactly reproduce the original random variable for the system observable (probability reproducibility). While agreement and reproducibility are mutually implied in the case of ideal measurement, finite thermodynamic resources constrain each of them. Starting from the third law of thermodynamics, we derive how the achievability of ideal intersubjectivity is affected by restricted thermodynamic resources. Specifically, we establish a no-go theorem concerning perfect intersubjectivity and present a deviation metric to account for the influence of limited resources. We further present attainable bounds for the agreement and bias that are exclusively dependent on the initial state of the environment. In addition, we show that either by cooling or coarse-graining, we can approximate ideal intersubjectivity even with finite resources. This work bridges quantum thermodynamics and the emergence of classicality in the form of intersubjectivity.

quant-ph↗

arXiv2026

Parameter estimation for quantum jump unraveling

We consider the estimation of parameters encoded in the measurement record of a continuously monitored quantum system in the jump unraveling, corresponding to a single-shot scenario, where information is continuously gathered. Here, it is generally difficult to assess the precision of the estimation procedure via the Fisher Information due to intricate temporal correlations and memory effects. In this paper we provide a full set of solutions to this problem. First, for multi-channel renewal processes we relate the Fisher Information to an underlying Markov chain and derive a easily computable expression for it. For non-renewal processes, we introduce a new algorithm that combines two methods: the monitoring operator method for metrology and the Gillespie algorithm which allows for efficient sampling of a stochastic form of the Fisher Information along individual quantum trajectories. We show that this stochastic Fisher Information satisfies useful properties related to estimation on a single run. Finally, we consider the case where some information is lost in data compression/post-selection and provide tools for computing the Fisher Information in this case. All scenarios are illustrated with instructive examples from quantum optics and condensed matter.

quant-ph↗

arXiv2026

Thermodynamic criteria for signaling in quantum channels

Signaling quantum channels are fundamental to quantum communication, enabling the transfer of information from input to output states. In contrast, thermalisation erases information about the initial state. This raises a crucial question: How does the thermalising tendency of a quantum channel constrain its signaling power and vice versa? In this work, we address this question by considering three thermodynamic tasks associated with a quantum channel: the generation, preservation, and transmission of athermality. We provide faithful measures for athermality generation and athermality preservation of quantum channels, and prove that their difference quantifies athermality transmission. Analysing these thermodynamic tasks, we find that the signaling ability of a quantum channel is upper-bounded by its athermality preservation and lower-bounded by its athermality transmission, thereby establishing a fundamental relationship between signaling and thermodynamic properties of channels for quantum communication. We demonstrate this interplay for the example of the quantum switch, revealing an explicit trade-off between the signaling ability and athermality of the quantum channels it can implement.

quant-ph↗

arXiv2025

Quantum measurements and equilibration: the emergence of objective outcomes via entropy maximisation

The measurement postulate of quantum theory stands in conflict with the laws of thermodynamics and has evoked debate regarding what actually constitutes a measurement. With the help of modern quantum statistical mechanics, we take the first step in formalising the hypothesis that quantum measurements are driven by the natural tendency of closed systems to maximize entropy, a notion that we call the Measurement-Equilibration Hypothesis. In this paradigm, we investigate how classical measurement outcomes can emerge within a purely unitary framework, and find that: (i) the interactions used in standard measurement models fail to spontaneously encode information classically and (ii) while ideal projective measurements are impossible, one can (for a given form of Hamiltonian) approximate them exponentially well as more physical systems are collected together into an ``observer'' system. We thus lay the groundwork for self-contained models of quantum measurement, proposing improvements to our simple scheme.

quant-ph↗

arXiv2025

Anomalous discharging of quantum batteries: the ergotropic Mpemba effect

Anomalous thermal relaxation is ubiquitous in nonequilibrium statistical mechanics. An emblematic example of this is the Mpemba effect, where an initially ``hot'' system cools faster than an initially ``cooler'' one. This effect has recently been studied in a variety of different classical and quantum settings. In this Letter, we find a novel signature of the Mpemba effect in the context of quantum batteries. We identify situations where batteries in higher charge states can discharge faster than less charged states. Specifically, we consider a quantum battery encoded in a single bosonic mode that is charged using unitary Gaussian operations. We show that the ergotropy, used here as a dynamical indicator of the energy stored in the battery, can be recast as a phase space relative entropy between the system's state and the unitarily connected passive state, at each time. Our formalism allows us to compute the ergotropy analytically under dissipative dynamics and allows us to understand the conditions which give rise to a Mpemba effect. We also find situations where two batteries charged to the same value using different operations can discharge at different rates.

quant-ph↗

arXiv2025

Precision bounds for multiple currents in open quantum systems

Thermodynamic (TUR) and kinetic (KUR) uncertainty relations are fundamental bounds constraining the fluctuations of current observables in classical, non-equilibrium systems. Several works have verified, however, violations of these classical bounds in open quantum systems, motivating the derivation of new quantum TURs and KURs that account for the role of quantum coherence. Here, we go one step further by deriving multidimensional KUR and TUR for multiple observables in open quantum systems undergoing Markovian dynamics. Our derivation exploits a multi-parameter metrology approach, in which the Fisher information matrix plays a central role. Crucially, our bounds are tighter than previously derived quantum TURs and KURs for single observables, precisely because they incorporate correlations between multiple observables. We also find an intriguing quantum signature of correlations that is captured by the off-diagonal element of the Fisher information matrix, which vanishes for classical stochastic dynamics. By considering two examples, namely a coherently driven qubit system and the three-level maser, we demonstrate that the multidimensional quantum KUR bound can even be saturated when the observables are perfectly correlated.

quant-ph↗

arXiv2024

Memory-minimal quantum generation of stochastic processes: spectral invariants of quantum hidden Markov models

Stochastic processes abound in nature and accurately modeling them is essential across the quantitative sciences. They can be described by hidden Markov models (HMMs) or by their quantum extensions (QHMMs). These models explain and give rise to process outputs in terms of an observed system interacting with an unobserved memory. Although there are infinitely many models that can generate a given process, they can vary greatly in their memory requirements. It is therefore of great fundamental and practical importance to identify memory-minimal models. This task is complicated due to both the number of generating models, and the lack of invariant features that determine elements of the set. In general, it is forbiddingly difficult to ascertain that a given model is minimal. Addressing this challenge, we here identify spectral invariants of a process that can be calculated from any model that generates it. This allows us to determine strict bounds on the quantum generative complexity of the process -- its minimal memory requirement. We then show that the bound is raised quadratically when we restrict to classical operations. This is an entirely quantum-coherent effect, as we express precisely, using the resource theory of coherence. Finally, we demonstrate that the classical bound can be violated by quantum models.

quant-ph↗

arXiv2024

Gillespie algorithm for quantum jump trajectories

The jump unravelling of a quantum master equation decomposes the dynamics of an open quantum system into abrupt jumps, interspersed by periods of coherent dynamics when no jumps occur. Such open quantum systems are ubiquitous in quantum optics and mesoscopic physics, hence the need for efficient techniques for their stochastic simulation. Numerical simulation techniques fall into two main categories. The first splits the evolution into small timesteps and determines stochastically for each step if a jump occurs or not. The second, known as Monte Carlo Wavefunction simulation, is based on the reduction of the norm of an initially pure state in the conditional no-jump evolution. It exploits the fact that the purity of the state is preserved by the finest unraveling of the master equation. In this work, we present an alternative method for the simulation of the quantum jump unraveling, inspired by the classical Gillespie algorithm. The method is particularly well suited for situations in which a large number of trajectories is required for relatively small systems. It allows for non-purity-preserving dynamics, such as the ones generated by partial monitoring and channel merging. We describe the algorithm in detail and discuss relevant limiting cases. To illustrate it, we include four example applications of increasing physical complexity and discuss the performance of the algorithm across regimes of interest for open quantum systems simulation. Publicly available implementations of our code are provided in Julia and Mathematica.

quant-ph↗

arXiv2024

Thermodynamic Overfitting and Generalization: Energetic Limits on Predictive Complexity

Efficiently harvesting thermodynamic resources requires a precise understanding of their structure. This becomes explicit through the lens of information engines -- thermodynamic engines that use information as fuel. Maximizing the work harvested using available information is a form of physically-instantiated machine learning that drives information engines to develop complex predictive memory to store an environment's temporal correlations. We show that an information engine's complex predictive memory poses both energetic benefits and risks. While increasing memory facilitates detection of hidden patterns in an environment, it also opens the possibility of thermodynamic overfitting, where the engine dissipates additional energy in testing. To address overfitting, we introduce thermodynamic regularizers that incur a cost to engine complexity in training due to the physical constraints on the information engine. We demonstrate that regularized thermodynamic machine learning generalizes effectively. In particular, the physical constraints from which regularizers are derived improve the performance of learned predictive models. This suggests that the laws of physics jointly create the conditions for emergent complexity and predictive intelligence.

cond-mat.stat-mech↗

arXiv2024

Trade-offs between precision and fluctuations in charging finite-dimensional quantum batteries

Within quantum thermodynamics, many tasks are modelled by processes that require work sources represented by out-of-equilibrium quantum systems, often dubbed quantum batteries, in which work can be deposited or from which work can be extracted. Here we consider quantum batteries modelled as finite-dimensional quantum systems initially in thermal equilibrium that are charged via cyclic Hamiltonian processes. We present optimal or near-optimal protocols for $N$ identical two-level systems and individual $d$-level systems with equally spaced energy gaps in terms of the charging precision and work fluctuations during the charging process. We analyze the trade-off between these figures of merit as well as the performance of local and global operations.

quant-ph↗

arXiv2023

Non-Ideal Measurement Heat Engines

We discuss the role of non-ideal measurements within the context of measurement engines by contrasting examples of measurement engines which have the same work output but with varying amounts of entanglement. Accounting for the cost of resetting, correlating the engine to a pointer state and also the cost of cooling the pointer state, we show that for a given work output, thermally correlated engines can outperform corresponding entanglement engines. We also show that the optimal efficiency of the thermally correlated measurement engine is achieved with a higher temperature pointer than the pointer temperature of the optimal entanglement engine.

quant-ph↗

arXiv2023

Fisher information of correlated stochastic processes

Many real-world tasks include some kind of parameter estimation, i.e., determination of a parameter encoded in a probability distribution. Often, such probability distributions arise from stochastic processes. For a stationary stochastic process with temporal correlations, the random variables that constitute it are identically distributed but not independent. This is the case, for instance, for quantum continuous measurements. In this paper we prove two fundamental results concerning the estimation of parameters encoded in a memoryful stochastic process. First, we show that for processes with finite Markov order, the Fisher information is always asymptotically linear in the number of outcomes, and determined by the conditional distribution of the process' Markov order. Second, we prove with suitable examples that correlations do not necessarily enhance the metrological precision. In fact, we show that unlike for entropic information quantities, in general nothing can be said about the sub- or super-additivity of the joint Fisher information, in the presence of correlations. We discuss how the type of correlations in the process affects the scaling. We then apply these results to the case of thermometry on a spin chain.

quant-ph↗